The azimuthal effective-index method

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Abstract
An approximate technique to solve guidance problems in dielectric waveguides having almost arbitrary cross-section index distribution is presented. The technique consists of reducing the solution of the three-dimensional guide to the solution of two unidimensional slabs. By starting with the circular-cylinder coordinate system instead of the Cartesian one, the results are found to be more precise and far more informative than those derived from any other approximate analytical technique. The ideas presented here may be easily extended to solve more sophisticated structures such as couplers and cavities.<>